abstract = "The distance between pairs of individuals is a useful
concept in the study of evolutionary algorithms. It is
particularly useful to define a distance which is
coherent with, i.e. related to, the action of a
particular operator. We present the first formal,
general definition of this operator-distance coherence.
We also propose a new distance function, based on the
multi-step transition probability (MSTP), that is
coherent with any GP operator for which the one-step
transition probability (1STP) between individuals can
be defined. We give an algorithm for 1STP in the case
of subtree mutation. Because MSTP is useful in GP
investigations, but impractical to compute, we evaluate
a variety of means to approximate it. We show that some
syntactic distance measures give good approximations,
and attempt to combine them to improve the
approximation using a GP symbolic regression method. We
conclude that 1STP itself is a sufficient indicator of
MSTP for subtree mutation.",